Thanks guys. Interesting feedback.
Regardless of individual company SOPs, it is clear now that there is nothing in the Airbus procedures prohibiting it.
@pineteam
It often happens that an aircraft arrives within a few minutes of the next departure; in such cases, the previous crew leaves the APU running to save APU start cycles. Therefore, we cannot assume whether they left it ON or the engineering switched it ON. Even if its engineering that did it, it's still a part of FCOM procedure and a change of crew definitely necessitates a fire test.
The point of asking this question was due to the fact that I was recently confronted by a Captain who asked me to prove where its written. I pointed out there's nothing prohibiting it, and with back to back flights with crew change, sometimes the APU remains ON continuously.
Apparently some people have their own interpretations of the FCOM. Not everything is mentioned nor can be mentioned explicitly for every situation. Thats how it works.